Simultaneous equations y1=ay2+B1=1+l ◆y2=ny1+B2x2+12 Economics 20- Prof anderson
Economics 20 - Prof. Anderson 1 Simultaneous Equations y1 = a1 y2 + b1 z1 + u1 y2 = a2 y1 + b2 z2 + u2
Simultaneity o Simultaneity is a specific type of endogeneity problem in which the explanatory variable is jointly determined with the dependent variable o As with other types of endogeneity, IV estimation can solve the problem o Some special issues to consider with simultaneous equations modelS (SEM) Economics 20- Prof anderson
Economics 20 - Prof. Anderson 2 Simultaneity Simultaneity is a specific type of endogeneity problem in which the explanatory variable is jointly determined with the dependent variable As with other types of endogeneity, IV estimation can solve the problem Some special issues to consider with simultaneous equations models (SEM)
Supply and demand example o Start with an equation you' d like to estimate, say a labor supply function ◆h。=anw+B+u, where S w is the wage and z is a supply shifter Call this a structural equation -it's derived from economic theory and has a causal interpretation where w directly affects hs Economics 20- Prof anderson
Economics 20 - Prof. Anderson 3 Supply and Demand Example Start with an equation you’d like to estimate, say a labor supply function hs = a1w + b1 z + u1 , where w is the wage and z is a supply shifter Call this a structural equation – it’s derived from economic theory and has a causal interpretation where w directly affects hs
Example(cont) Problem that cant just regress observed hours on wage, since observed hours are determined by the equilibrium of supply and demand Consider a second structural equation. in this case the labor demand function ◆hnt=21+l2 d by So hours are determined a seM Economics 20- Prof anderson 4
Economics 20 - Prof. Anderson 4 Example (cont) Problem that can’t just regress observed hours on wage, since observed hours are determined by the equilibrium of supply and demand Consider a second structural equation, in this case the labor demand function hd = a2w + u2 So hours are determined by a SEM
Example(cont) o Both h and w are endogenous because they are both determined by the equilibrium of supply and demand o z is exogenous, and it's the availability of this exogenous supply shifter that allows us to identify the structural demand equation o With no observed demand shifters, supply is not identified and cannot be estimated Economics 20- Prof anderson 5
Economics 20 - Prof. Anderson 5 Example (cont) Both h and w are endogenous because they are both determined by the equilibrium of supply and demand z is exogenous, and it’s the availability of this exogenous supply shifter that allows us to identify the structural demand equation With no observed demand shifters, supply is not identified and cannot be estimated